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advanced-math

A radioactive substance has a half-life of 5 years. If you start with 80 grams, how much remains after 10 years?

A

20 grams

B

40 grams

C

10 grams

D

5 grams

Correct Answer: A

Choice A is the correct answer. Apply the half-life concept.

  1. Half-lives: 10 years ÷ 5 years = 2 half-lives.
  2. After 1st half-life (5 years): 80×0.5=4080 \times 0.5 = 40 grams.
  3. After 2nd half-life (10 years): 40×0.5=2040 \times 0.5 = 20 grams.
  4. Formula: A(t)=80(0.5)t/5=80(0.5)2=20A(t) = 80(0.5)^{t/5} = 80(0.5)^2 = 20.

💡 Strategic Tip: Number of half-lives = elapsed time ÷ half-life period.

Choice B is incorrect because this is after only 1 half-life (5 years). Choice C is incorrect because this would be after 3 half-lives (15 years). Choice D is incorrect because this would be after 4 half-lives (20 years).